Abstract

A self-focusing is observed that arises from a purely second-order nonlinear susceptibility in a phase-matched second-harmonic-generation experiment. Control of the magnitude and sign of the intensity-dependent phase shift is accomplished through a dispersion external to the nonlinear medium. Analytical expressions characterizing the self-focusing and chirp on both beams in the two-wave parametric interaction are presented and compared with experimental values.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
    [CrossRef]
  2. H. J. Bakker, P. C. M. Planken, L. Kuipers, A. Lagendijk, Phys. Rev. A 42, 4085 (1990).
    [CrossRef] [PubMed]
  3. R. DeSalvo, D. J. Hagen, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, Opt. Lett. 17, 28 (1992).
    [CrossRef] [PubMed]
  4. X. M. Zhao, D. J. McGraw, IEEE J. Quantum Electron. 28, 930 (1992).
    [CrossRef]
  5. J. M. Yarborough, J. Falk, Appl. Phys. Lett. 18, 70 (1971).
    [CrossRef]
  6. K. A. Stankov, Appl. Phys. B 45, 191 (1988).
    [CrossRef]
  7. C. Hu, J. R. Whinnery, Appl. Opt. 12, 72 (1973).
    [CrossRef] [PubMed]
  8. CVI Optics, Inc., 200 Dorado Place, Albuquerque, N.M.
  9. D. E. Spence, P. N. Kean, W. Sibbett, Opt. Lett. 16, 42 (1991).
    [CrossRef] [PubMed]

1992 (2)

1991 (1)

1990 (1)

H. J. Bakker, P. C. M. Planken, L. Kuipers, A. Lagendijk, Phys. Rev. A 42, 4085 (1990).
[CrossRef] [PubMed]

1988 (1)

K. A. Stankov, Appl. Phys. B 45, 191 (1988).
[CrossRef]

1973 (1)

1971 (1)

J. M. Yarborough, J. Falk, Appl. Phys. Lett. 18, 70 (1971).
[CrossRef]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Bakker, H. J.

H. J. Bakker, P. C. M. Planken, L. Kuipers, A. Lagendijk, Phys. Rev. A 42, 4085 (1990).
[CrossRef] [PubMed]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

DeSalvo, R.

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Falk, J.

J. M. Yarborough, J. Falk, Appl. Phys. Lett. 18, 70 (1971).
[CrossRef]

Hagen, D. J.

Hu, C.

Kean, P. N.

Kuipers, L.

H. J. Bakker, P. C. M. Planken, L. Kuipers, A. Lagendijk, Phys. Rev. A 42, 4085 (1990).
[CrossRef] [PubMed]

Lagendijk, A.

H. J. Bakker, P. C. M. Planken, L. Kuipers, A. Lagendijk, Phys. Rev. A 42, 4085 (1990).
[CrossRef] [PubMed]

McGraw, D. J.

X. M. Zhao, D. J. McGraw, IEEE J. Quantum Electron. 28, 930 (1992).
[CrossRef]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Planken, P. C. M.

H. J. Bakker, P. C. M. Planken, L. Kuipers, A. Lagendijk, Phys. Rev. A 42, 4085 (1990).
[CrossRef] [PubMed]

Sheik-Bahae, M.

Sibbett, W.

Spence, D. E.

Stankov, K. A.

K. A. Stankov, Appl. Phys. B 45, 191 (1988).
[CrossRef]

Stegeman, G.

Van Stryland, E. W.

Whinnery, J. R.

Yarborough, J. M.

J. M. Yarborough, J. Falk, Appl. Phys. Lett. 18, 70 (1971).
[CrossRef]

Zhao, X. M.

X. M. Zhao, D. J. McGraw, IEEE J. Quantum Electron. 28, 930 (1992).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

K. A. Stankov, Appl. Phys. B 45, 191 (1988).
[CrossRef]

Appl. Phys. Lett. (1)

J. M. Yarborough, J. Falk, Appl. Phys. Lett. 18, 70 (1971).
[CrossRef]

IEEE J. Quantum Electron. (1)

X. M. Zhao, D. J. McGraw, IEEE J. Quantum Electron. 28, 930 (1992).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Phys. Rev. A (1)

H. J. Bakker, P. C. M. Planken, L. Kuipers, A. Lagendijk, Phys. Rev. A 42, 4085 (1990).
[CrossRef] [PubMed]

Other (1)

CVI Optics, Inc., 200 Dorado Place, Albuquerque, N.M.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Schematic for the double-pass second-harmonic-generation experiment used to generate and detect the parametric lens. HBS, harmonic beam splitter; M1, fundamental mirror; M2, second-harmonic mirror; GW, glass wedge; PD-Y, power detection photodiode; PD-X, center intensity detection photodiode.

Fig. 2
Fig. 2

Double-pass fundamental and second-harmonic powers simultaneously recorded during a scan of the interpass phase shift Θ′. The parametric self-focusing is maximized at integer values of π, midway between the power extrema.

Fig. 3
Fig. 3

Power-versus-center-intensity plots recorded as Θ′ was scanned. The nonzero phase shifts observed between power and center intensity are caused by the parametric lens. The narrower ellipses in both figures result from opening the iris to measure the instrumental contribution to the phase shift.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

d ρ 1 / d z = K ρ 2 ρ 1 sin Θ ,
d ρ 2 / d z = K ρ 1 2 sin Θ ,
d ϕ 1 / d z = K ρ 2 cos Θ ,
d ϕ 2 / d z = K ρ 1 2 cos Θ / ρ 2 .
ρ 1 = r 1 ρ 1 0 [ 1 ( 1 + 2 r 2 sin Θ + r 1 2 ) η 2 / 2 ] ,
ρ 2 = η ρ 1 0 [ r 2 + ( 1 η 2 / 2 ) r 1 2 sin Θ ] ,
ϕ 1 = ϕ 1 + r 2 η 2 cos Θ ,
ϕ 2 = ϕ 2 2 K ( r 1 ρ 1 0 ) ( 1 η 2 ) cos Θ / ρ 2 = ϕ 2 ( z / L ) r 1 2 cos Θ ( 1 η 2 ) / r 2 .
β = 16 r 2 ln 2 η 2 cos Θ / ( t FWHM ) 2 ,
1 / f = 4 2 η 2 r 2 cos Θ / k 1 w 2 2 = 2 2 η 2 / Z R ,
I ( beam center ) = P / π w 0 2 = [ A r 1 2 ( ρ 1 0 ) 2 / π w 0 2 ] { 1 η 2 [ 1 + 2 r 2 × ( sin Θ + cos Θ ) + r 1 2 ] } ,

Metrics